Three times in the 1920s and 30s, the Olympics gave out medals for alpinism, AKA mountain climbing. No, it's not as absurd as giving out medals for art (see the Isaac Israels profile), but it's up there.
Alas, competitors did not have to race up a nearby mountain and hoist a flag quicker than others. Instead, medals for given for the most important mountaineering achievement of the past four years. For example, in 1924, it went to a team of Brits and seven sherpas who tried to scale Mount Everest. The key word is "tried". All the sherpas died.
In 1936, the medal went to a German-born Swiss married couple of Gunter and Hettie Dyhrenfurth. To the disdain of Nazi organizers, both were part Jewish; he a quarter, she a half. In 1930, Gunter climbed Jongsong, the highest scaled peak at the time. In 1934, at the top of Sia Kangri, Hettie became the highest woman ever, a record she kept until the 1950s.
Hettie was the first and last woman to medal in alpinism. The IOC decided that "presenting of prizes for mountain climbing encourages young people to undertake dangerous exploits".
Oh, and in the same Olympics, Gunther also participated in the literature competition.
Now that's absurd...